Instabilities, Chaos and Turbulence

Instabilities, Chaos and Turbulence PDF

Author: Paul Manneville

Publisher: World Scientific

Published: 2010

Total Pages: 456

ISBN-13: 1848163924

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This book (2nd edition) is a self-contained introduction to a wide body of knowledge on nonlinear dynamics and chaos. Manneville emphasises the understanding of basic concepts and the nontrivial character of nonlinear response, contrasting it with the intuitively simple linear response. He explains the theoretical framework using pedagogical examples from fluid dynamics, though prior knowledge of this field is not required. Heuristic arguments and worked examples replace most esoteric technicalities. Only basic understanding of mathematics and physics is required, at the level of what is currently known after one or two years of undergraduate training: elementary calculus, basic notions of linear algebra and ordinary differential calculus, and a few fundamental physical equations (specific complements are provided when necessary). Methods presented are of fully general use, which opens up ample windows on topics of contemporary interest. These include complex dynamical processes such as patterning, chaos control, mixing, and even the Earth's climate. Numerical simulations are proposed as a means to obtain deeper understanding of the intricacies induced by nonlinearities in our everyday environment, with hints on adapted modelling strategies and their implementation.

Instabilities, Chaos And Turbulence (2nd Edition)

Instabilities, Chaos And Turbulence (2nd Edition) PDF

Author: Paul Manneville

Publisher: World Scientific

Published: 2010-07-21

Total Pages: 456

ISBN-13: 1911299409

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This book (2nd edition) is a self-contained introduction to a wide body of knowledge on nonlinear dynamics and chaos. Manneville emphasises the understanding of basic concepts and the nontrivial character of nonlinear response, contrasting it with the intuitively simple linear response. He explains the theoretical framework using pedagogical examples from fluid dynamics, though prior knowledge of this field is not required. Heuristic arguments and worked examples replace most esoteric technicalities. Only basic understanding of mathematics and physics is required, at the level of what is currently known after one or two years of undergraduate training: elementary calculus, basic notions of linear algebra and ordinary differential calculus, and a few fundamental physical equations (specific complements are provided when necessary). Methods presented are of fully general use, which opens up ample windows on topics of contemporary interest. These include complex dynamical processes such as patterning, chaos control, mixing, and even the Earth's climate. Numerical simulations are proposed as a means to obtain deeper understanding of the intricacies induced by nonlinearities in our everyday environment, with hints on adapted modelling strategies and their implementation./a

Nonlinear Instability, Chaos, and Turbulence

Nonlinear Instability, Chaos, and Turbulence PDF

Author: Lokenath Debnath

Publisher: Computational Mechanics

Published: 1998

Total Pages: 432

ISBN-13:

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The second volume in a study of nonlinear stability, chaos and turbulence. It demonstrates the importance of mathematical, computational and experimental techniques to the advancement of research in nonlinear instability, chaotic motions and turbulent flow systems.

Turbulence and Instabilities

Turbulence and Instabilities PDF

Author: O.M. Belotserkovskii

Publisher:

Published: 2000

Total Pages: 364

ISBN-13:

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Monograph presents the newest results in the numerical modeling and computer simulation of turbulence.

Turbulence and Structures

Turbulence and Structures PDF

Author: Herman Branover

Publisher: Academic Press

Published: 1999

Total Pages: 296

ISBN-13: 9780121257408

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Turbulence is one of the most wide-spread phenomena in the universe. It relates to processes within the atmosphere, ocean, deep within the earth, as well as to the stars. The general public usually knows about turbulence from the unpleasant shaking of an airplane, or from disastrous atmospheric phenomena such as typhoons and hurricanes. The chaotic and unpredictable behavior of turbulent movement makes it very difficult to study. The degree of understanding of turbulence is still far from being complete. Some progress was made with the recent advent of a new science--chaos theory. The authors succeeded in examining one basic feature of turbulence called helicity (or spirality) which is the foundation of explaining and predicting the generation of large turbulent structures (e.g. typhoons). Helicity is a universal feature existing not only in fluid flows but also in solid bodies and even in living organisms. This book can be especially useful for researchers and students in fluid mechanics, plasma, geophysics, biology, and meteorology. * Examines the helical mechanism of self-organization in nature and laboratory * Presents a unified approach to chaos and theory * Discusses similarities and differences in the formation of dynamic and magnetic structures * Successfully combines profound theoretical and experimental knowledge * Includes a disk with an expanded bibliographical database

Dissipative Structures and Weak Turbulence

Dissipative Structures and Weak Turbulence PDF

Author:

Publisher: Academic Press

Published: 2014-06-28

Total Pages: 505

ISBN-13: 008092445X

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Dissipative Structure and Weak Turbulence provides an understanding of the emergence and evolution of structures in macroscopic systems. This book discusses the emergence of dissipative structures. Organized into 10 chapters, this book begins with an overview of the stability of a fluid layer with potentially unstable density stratification in the field of gravity. This text then explains the theoretical description of the dynamics of a given system at a formal level. Other chapters consider several examples of how such simplified models can be derived, complicating the picture progressively to account for other phenomena. This book discusses as well the theory and experiments on plain Rayleigh–Bénard convection by setting first the theoretical frame and deriving the analytical solution of the marginal stability problem. The final chapter deals with building a bridge between chaos as studied in weakly confined systems and more advanced turbulence in the most conventional sense. This book is a valuable resource for physicists.

Physics of Buoyant Flows

Physics of Buoyant Flows PDF

Author: Verma Mahendra Kumar

Publisher: World Scientific

Published: 2018-05-30

Total Pages: 352

ISBN-13: 9813237813

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Gravity pervades the whole universe; hence buoyancy drives fluids everywhere including those in the atmospheres and interiors of planets and stars. Prime examples of such flows are mantle convection, atmospheric flows, solar convection, dynamo process, heat exchangers, airships and hot air balloons. In this book we present fundamentals and applications of thermal convection and stratified flows. Buoyancy brings in extremely rich phenomena including waves and instabilities, patterns, chaos, and turbulence. In this book we present these topics in a systematic manner. First we present a unified treatment of linear theory that yields waves and thermal instability for stably and unstably-stratified flows respectively. We extend this analysis to include rotation and magnetic field. We also describe nonlinear saturation and pattern formation in Rayleigh-Bénard convection. The second half of the book is dedicated to buoyancy-driven turbulence, both in stably-stratified flow and in thermal convection. We describe the spectral theory including energy flux and show that the thermally-driven turbulence is similar to hydrodynamic turbulence. We also describe large-scale quantities like Reynolds and Nusselt numbers, flow anisotropy, and the dynamics of flow structures, namely flow reversals. Thus, this book presents all the major aspects of the buoyancy-driven flows in a coherent manner that would appeal to advanced graduate students and researchers.

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